Pausing a video comp with slider control

If you added a checkbox to your Controls layer, you could use an expression like this for the time remapping of your first video layer:

p = thisComp.layer("Controls").effect("Checkbox Control")("Checkbox");
t = p.value ? time : 0;
if (p.numKeys > 0){
  n = p.nearestKey(time).index;
  if (p.key(n).time > time) n--;
  if (n > 0){
    t = p.key(1).value ? p.key(1).time : 0;
    t += p.value ? time - p.key(n).time : 0;
    for (i = 2; i <= n; i++){
      t += p.key(i-1).value ? p.key(i).time - p.key(i-1).time : 0;
    }
  }
}
t

The first video layer will run while the checkbox is on. Then you could add an expression like this to the time remapping of your second video layer:

time - thisComp.layer("Screen switch 1").timeRemap;

which will cause the second video layer to run whenever the first video layer is paused. Or, you could control the second video layer with its own checkbox so that you could control the two layers independently.